import itertools
from math import sin, cos, radians, atan2, sqrt, pi, degrees

instructions = []

with open("12.input") as f:
    for line in f.readlines():
        line = line.strip()
        instructions.append((line[0], int(line[1:])))

myadd = lambda xs,ys: tuple(x + y for x, y in zip(xs, ys))

def manhattan_distance(pos):
    (x, y) = pos
    return abs(y) + abs(x)

def move(position, angle, instruction):
    op, arg = instruction

    if op == 'L':
        angle += arg
    elif op == 'R':
        angle -= arg
    elif op == 'N':
        position = myadd(position, (0, arg))
    elif op == 'S':
        position = myadd(position, (0, -arg))
    elif op == 'E':
        position = myadd(position, (arg, 0))
    elif op == 'W':
        position = myadd(position, (-arg, 0))
    elif op == 'F':
        position = myadd(position, (cos(radians(angle)) * arg, sin(radians(angle)) * arg))

    return (position, angle)

position = (0, 0)
angle = 0

for instruction in instructions:
    (position, angle) = move(position, angle, instruction)

print("Answer 1: {:0.0f}".format(manhattan_distance(position)))

def print_vector(vec):
    print("{}, {}".format(vec, degrees(atan2(vec[1], vec[0]))))


def rotate(vec, degrees):
    angle = atan2(vec[1], vec[0])
    length = sqrt(vec[0] ** 2 + vec[1] ** 2)
    angle += radians(degrees)
    vec = (cos(angle) * length, sin(angle) * length)
    return vec


def move_waypoint(ship_pos, way_pos, instruction):
    op, arg = instruction

    if op == 'L':
        way_pos = rotate(way_pos, arg)
    elif op == 'R':
        way_pos = rotate(way_pos, -arg)
    elif op == 'N':
        way_pos = myadd(way_pos, (0, arg))
    elif op == 'S':
        way_pos = myadd(way_pos, (0, -arg))
    elif op == 'E':
        way_pos = myadd(way_pos, (arg, 0))
    elif op == 'W':
        way_pos = myadd(way_pos, (-arg, 0))
    elif op == 'F':
        ship_pos = (ship_pos[0] + way_pos[0] * arg, ship_pos[1] + way_pos[1] * arg)

    return (ship_pos, way_pos)

ship_pos = (0, 0)
way_pos = (10, 1)

for instruction in instructions:
    (ship_pos, way_pos) = move_waypoint(ship_pos, way_pos, instruction)

print("Answer 2: {:0.0f}".format(manhattan_distance(ship_pos)))